Abstract: Injection molding is one of the most important polymer processing operations. The results from numerical simulation of this process provide valuable information in designing part/ mold or choosing process parameters. The flow simulation is based on a hybrid finite-element/ finite-difference numerical solution of the generalized Hele-Shaw flow of a non - Newtonian fluid under non - isothermal condition. A unified expression in terms of flow rate is set up for both entrance and interior nodes. In advancing the melt front , the commonly used method of determining time step is modified. Two examples are given to show the validity of the numerical method.